Energy-momentum tensor of special relativistic fluids and Connection of relativistic and non-relativistic fluids in the new scaling

TL;DR

This paper introduces an iso-dimension scale for relativistic fluids, calculates tensor components in various coordinate systems, and explores the connection between relativistic and non-relativistic fluids, highlighting key distinctions.

Contribution

It develops an iso-dimension scale for relativistic fluids and derives tensor components, linking relativistic and non-relativistic fluid behaviors in a new framework.

Findings

Derived tensor components in cylindrical and spherical coordinates.

Established the limit of relativistic tensors to non-relativistic forms.

Highlighted differences such as shear stress and heat flux origins.

Abstract

In this paper, the relativistic fluids with the negligible magnetic field in the flat metric are studied. The iso-dimension scale in introduced, in this scale, all similar components of a variable have the same dimension. Also, the components of shear, bulk and heat flux tensors and the components of energy-momentum tensors are calculated in the cylindrical and spherical coordinate systems, all these components are derived in the iso-dimension scale. The non-relativistic shear, bulk and heat flux tensors and the components of energy-momentum tensor are derived in the limit of the relativistic fluids. Also, the connection of relativistic and non-relativistic fluids are seen. So, some distinctions of relativistic and non-relativistic fluids are displayed, for example in the relativistic fluids, the time derivative of velocity is created the shear stress tensor and derivative of velocity and temperature is created the heat flux energy-momentum tensor, etc.